Scale a 3D beveled bezier path vertex on 1 axis, not 3
When you scale a control point you're scaling its radius around the curve, which is inherently circular. The only way to get a flat profile is to use a second bevel object with a thin rectangular shape. Once you apply that bevel object, scaling the cp radius only affects width in the way you want.

In my example, I found a better result with a low curve resolution (4-5), and then applying a subdiv modifier with level 3.